First, Spira hints that there is a set of spells which, together, account for some, or all, of the dungeon randomization. This ties in with the text from the statue...
Suggesting, to me, that one spell judges how well rooms fit with the overall layout nearby, removing the ones that it deems unacceptable (if one of the factors is how long the room has been there, it would ensure that all rooms eventually cycle out). From my interpretation, unfit rooms are flushed into sub-dungeons, and the space where the room was is queued for the room generator spell. Additionally, it seems that there are some pre-generated rooms (perhaps rooms that were flushed recently?), which are used if available, and otherwise completely new rooms have to be generated instead.
Also note that shortly after the statue talks about replacing (3, 3, 4), it mentions Third Sibling moving towards it (from (3, 5, 4) to (3, 4, 4)), so it probably prioritizes replacing rooms that either have been visited recently (if First Sibling is returning from somewhere, and had to solve a puzzle or something on the way through the first time), or areas which are poor fits and a character is nearby, so may visit soon).
This suggests a limited or nonexistant ability to process multiple spells concurrently, or that many of the usually-active spells would interfere with the entry protocol.
(Side note: The statue's eyes change color from red+white to green+red
here)
Next, recall the spear and skill tree, lost shortly after first visiting DL2?
Consider how it reappears, far later, in a separate room, also on DL2:
Going back to the first Spira quote, "Spells working in tandem keep all the rooms random:
Items scattered, dead ends seldom...", it is fairly obvious that part of the room randomization process takes items from flushed rooms and places them into rooms generated later on. This ties in nicely with the healer's quest for the ruby: It was dropped in a room that was probably flushed shortly afterwards, so to get back to it would require finding where the generator placed it next (or maybe it remained in the room, in a sub-D, until the room/sub-D was destroyed entirely (if that happens?), or the room was re-used elsewhere on DL2 (if sub-D'd rooms are re-used later).
Finally, from that, some less-plausible speculation: The lights seen below could be the spells activating and deactivating in turn, forming a vast magi-computer which controls the dungeon levels of the warrens (less, or no, control over the underside?). One of the more active spell-processes is likely what keeps Sinful chained in the DL3 boss room.
When he shut off the power, the background was very similar to the background where the colored lights were (except with an ominous red gradient, and zoomed out to show far more complexity), and did not have any lights visible on it (though it's hard to be sure, as when the power was on, Sinful's room was lit green, with a solid background). (Also note: When the power returned, there was a brief .gif where it rapidly flashed between the lines being red and grey, though that may have just been part of the visual effects at the time)